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Adding and Subtracting Integers/Transcript
Transcript Title text reads, The Mysteries of Life with Tim and Moby. A boy, Tim, and his robot friend Moby are hiking up a steep mountain next to a lake. Moby pushes ahead as Tim gasps for air. Tim: Boy… would you look at that… view! Hey… how much further is it? On-screen, Tim stands still, with sweat running down his face. Moby beeps. He pulls out a map, which shows a side-view of the mountain, as well as a lake at the bottom. Moby points to a spot on the map showing that they are only halfway to the top. Tim: Huh. What do you say we, uh, take a little break for a letter? On-screen, a letter appears. Text reads as Tim narrates: Dear Tim and Moby, we start adding and subtracting integers tomorrow. That seems so easy. What's the point? From: Caleb. On-screen, Tim sits down on a rock. Tim: Well, integers are like the good ol’ regular whole numbers we use everyday, so I suppose adding and subtracting them can be pretty easy. A label appears, reading, integers. Another label reads, whole numbers. Tim: But there’s one catch: Unlike whole numbers, integers can be positive or negative! Text fills the screen, reading, integers. A plus sign and a minus sign appear. Tim: You probably add and subtract positive integers all day long without even realizing it. On-screen, a boy and a girl are sitting at a table. Eight pieces of candy are on the table in front of each child. The boy takes three pieces of candy from the girl. He smiles. An equation above his head reads: 8 plus 3 equals 11. The girl is upset. An equation above her head reads, 8 minus 3 equals 5. Tim: But when you’re dealing with negative integers, it’s a bit trickier. This is where a number line comes in handy. A label appears, reading, number line. A number line appears, stretching from negative 10 on the left to positive 10 on the right. Tim: Say we want to add negative 4 and negative 5. An equation above the number line reads: negative 4 plus negative 5. Tim: Negative 4 and negative 5 are both negative integers, so you know the answer will also be a negative integer… in this case, negative 9. On-screen, the number line displays negative 4 as 4 highlighted spaces to left of 0. Then 5 more spaces are highlighted farther to the left, extending to negative nine. An equation above the line reads: negative 4 plus negative 5 equals negative 9. Moby beeps. Tim: Good question. What if we add negative 4 and a positive 5? The equation above the number line changes to read, negative 4 plus 5. Tim: When you add a negative and a positive integer, the sum will have the sign of the integer with the greater absolute value, or distance from zero on the number line… in this case, the positive 5. A label appears, reading, absolute value. Negative 4 appears on the number line as four highlighted spaces to left of 0. To add positive 5, five spaces are counted to the right of negative 4, extending to positive 1. Tim: And our answer is positive 1. The equation above the number line reads, negative 4 plus 5 equals 1. Moby beeps. Tim: Well, think about it. 4 and negative 4 are additive inverses; they cancel each other out and their sum is always 0. On-screen, the equation above the number line changes to read, 4 plus negative 4 equals 0. A label reads, additive inverses. Tim: But we added one more than 4 so there was a 1 left over. And that gives us our answer! On-screen, the equation above the number line changes to read, 5 plus negative 4 equals 1. Moby beeps and points toward the top of the mountain. Tim doesn’t stand up. Tim: Ahhhh… wait, Moby, there's, uh, there's more explaining to do! On-screen, the number line appears without any highlighting on it. Tim: See, number lines are great when the numbers we’re dealing with are relatively small. But with bigger numbers, they don’t really help us so much. For these numbers, it’s better to keep in mind two key rules. First: Adding a negative number is like subtracting a positive one. A banner appears, reading, adding a negative number is like subtracting a positive one. TIM: Let’s say we hike up to 1,000 meters in altitude on this here mountain. On-screen, the map of the mountain and nearby lake appears. A point near the top of the mountain is labeled, 1,000 meters. Tim: But, as we’re going up, I drop my hat! On-screen, Tim’s hat appears on the map, a bit below the 1,000-meter mark. The hat is labeled, 200 meters. Tim: So I turn around and walk 200 meters down the slope to get it back. To figure out the position of my hat, we add a negative number, which is the same as subtracting a positive one. I got all the way up to 1,000 meters, but then I traveled 200 meters down the slope. On-screen, the hat's label changes to negative 200 meters. Tim: Since I reversed direction, I can write the 200 meters as a negative number. So 1,000 plus negative 200 equals… 800. An equation appears, reading, 1,000 meters plus negative 200 meters equals 800 meters. Tim's hat is labeled, 800 meters. Tim: So it’s the same as subtracting positive 200. The equation changes to 1,000 meters minus 200 meters equals 800. Moby beeps. Tim: Okay, the second rule: Subtracting a negative number is like adding a positive one. A banner appears, reading, subtracting a negative number is like adding a positive one. Tim: To see that, let’s try to figure out the difference in altitude between the top of this mountain and the bottom of that lake. On-screen, the map of the mountain and the nearby lake appears. Tim points to the top of the mountain and the bottom of the lake. Tim: That means subtracting a negative number. The mountain’s summit is 1,025 meters above sea level. That's a positive number. The lake’s bottom is 155 meters below sea level. On-screen, the top of the mountain is labeled, 1,025 meters above sea level. The base of the mountain is labeled, sea level. The bottom of the lake is labeled, 155 meters below sea level. Tim: We can treat that as a negative number, negative 155. Onscreen, the bottom of the lake is labeled, negative 155. Tim: If subtracting a negative number is the same as adding its inverse, then we can say that 1 minus negative 1 equals 1 plus 1. An equation appears, reading, 1 minus negative 1 equals 1 plus 1. Tim: So we can replace that minus negative 155 with a plus 155. An equation appears, reading, 1,025 minus negative 155. The equation changes to read, 1,025 plus 155. Tim: The difference in altitude is 1,180 meters! On-screen, the equation changes to read, 1,025 plus 155 equals 1,180. Moby beeps. Tim: Well, to express this as a general rule, we can say that a, minus negative b, equals a, plus b. A banner appears, reading, a, minus negative b, equals a, plus b. Tim: It’s a little tricky, but once you get the hang of it, it's easier than walking downhill. Which I'd like to be doing right now! Moby beeps and motions for Tim to continue walking upward. Tim: All right, all right. Category:BrainPOP Transcripts Category:BrainPOP Math Transcripts